domains and functions

Question

Let
f(x)=2x−5/x²−4x+c
Find the value of c if the domain of f(x) is
(−∞,−1)∪(−1,5)∪(5,∞)
Explain your thinking.

 

Note that the / means this is a fraction. Sorry but I couldn't write out the full fraction

Thanks!

Answer 1

Your domain indicates that you have vertical asymptotes at x=-1, and x=5.  We have vertical asymptotes when the denominator is zero. 

 

x² - 4x + c = 0

 

 

Factor the left side of the equation using FOIL to write the vertical asymptotes in factored form.

 

(x + 1)(x - 5) = 0

 

 

Now we expand the left side.  Note that when we expand, we will get -4x as a middle term in the denominator.

 

x² - 4x - 5 = 0

 

 

c = -5